Abstract: Topological phases are exotic states of quantum matter which are beyond the usual symmetry description. These phases have some interesting properties, such as robust ground state degeneracy that depends on the surface topology, quasiparticle fractional statistics, topological entanglement entropy, etc. Topological phases not only play a significant role in the basic scientific research of condensed matter physics, but also provide a natural medium for fault-tolerant quantum computation. Quantum simulation suggests that the complicated or inaccessible physical phenomena can be simulated by a controlled quantum system, which will provide a powerful means to explore topological phases and their topological properties. Nuclear magnetic resonance, as one physical implementation of quantum simulation, is a good test platform due to its sophisticated control and precise measurement in multi-qubit experiments. In this paper, topological phases and nuclear magnetic resonance quantum simulator are reviewed， and three related experiments on quantum simulation of topological phases are introcluced. Finally, a summary and an outlook towards topological quantum computation are given.

Key words: nuclear magnetic resonance, quantum simulation, topological phase, topological quantum phase transition, topological quantum computation